Problem: Simplify the following expression: $p = \dfrac{60q + 54}{60q}$ You can assume $q \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $60q + 54 = (2\cdot2\cdot3\cdot5 \cdot q) + (2\cdot3\cdot3\cdot3)$ The denominator can be factored: $60q = (2\cdot2\cdot3\cdot5 \cdot q)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $p = \dfrac{(6)(10q + 9)}{(6)(10q)}$ Dividing both the numerator and denominator by $6$ gives: $p = \dfrac{10q + 9}{10q}$